# floyd_warshall.py
"""
    The problem is to find the shortest distance between all pairs of vertices in a weighted directed graph that can
    have negative edge weights.
"""

from __future__ import print_function


def _print_dist(dist, v):
	print("\nThe shortest path matrix using Floyd Warshall algorithm\n")
	for i in range(v):
		for j in range(v):
			if dist[i][j] != float('inf') :
				print(int(dist[i][j]),end = "\t")
			else:
				print("INF",end="\t")
		print()



def floyd_warshall(graph, v):
	"""
    :param graph: 2D array calculated from weight[edge[i, j]]
    :type graph: List[List[float]]
    :param v: number of vertices
    :type v: int
    :return: shortest distance between all vertex pairs
    distance[u][v] will contain the shortest distance from vertex u to v.

    1. For all edges from v to n, distance[i][j] = weight(edge(i, j)).
    3. The algorithm then performs distance[i][j] = min(distance[i][j], distance[i][k] + distance[k][j]) for each
    possible pair i, j of vertices.
    4. The above is repeated for each vertex k in the graph.
    5. Whenever distance[i][j] is given a new minimum value, next vertex[i][j] is updated to the next vertex[i][k].
    """
		
	dist=[[float('inf') for _ in range(v)] for _ in range(v)]
	
	for i in range(v):
		for j in range(v):
			dist[i][j] = graph[i][j]

    # check vertex k against all other vertices (i, j)
	for k in range(v):
		# looping through rows of graph array
		for i in range(v):
			# looping through columns of graph array
			for j in range(v):
				if dist[i][k]!=float('inf') and dist[k][j]!=float('inf') and dist[i][k]+dist[k][j] < dist[i][j]:
					dist[i][j] = dist[i][k] + dist[k][j]

	_print_dist(dist, v)
	return dist, v

			

if __name__== '__main__':
	v = int(input("Enter number of vertices: "))
	e = int(input("Enter number of edges: "))

	graph = [[float('inf') for i in range(v)] for j in range(v)]

	for i in range(v):
		graph[i][i] = 0.0

    # src and dst are indices that must be within the array size graph[e][v]
    # failure to follow this will result in an error
	for i in range(e):
		print("\nEdge ",i+1)
		src = int(input("Enter source:"))
		dst = int(input("Enter destination:"))
		weight = float(input("Enter weight:"))
		graph[src][dst] = weight

	floyd_warshall(graph, v)


	# Example Input
	# Enter number of vertices: 3
	# Enter number of edges: 2

	# # generated graph from vertex and edge inputs
	# [[inf, inf, inf], [inf, inf, inf], [inf, inf, inf]]
	# [[0.0, inf, inf], [inf, 0.0, inf], [inf, inf, 0.0]]

	# specify source, destination and weight for edge #1
	# Edge  1
	# Enter source:1
	# Enter destination:2
	# Enter weight:2

	# specify source, destination and weight for edge #2
	# Edge  2
	# Enter source:2
	# Enter destination:1
	# Enter weight:1

	# # Expected Output from the vertice, edge and src, dst, weight inputs!!
	# 0		INF	INF
	# INF	0	2
	# INF	1	0
